A147605 Expansion of g.f.: 1/((1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7)*(1 + x + x^2 + x^3 + x^4 + x^5 - x^7)).

1, -1, 1, 0, 1, 1, 3, 3, 3, 10, 11, 21, 32, 52, 77, 128, 206, 320, 517, 817, 1297, 2060, 3290, 5220, 8298, 13205, 20980, 33360, 53056, 84366, 134114, 213263, 339086, 539123, 857240, 1363034, 2167197, 3445840, 5478951, 8711511, 13851359

Offset: 0

Author

Roger L. Bagula, Nov 08 2008

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,0,1,2,3,5,7,5,3,2,1,0,-1,-1).

Crossrefs

Cf. A107479, A147606, A147607, A147617.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x^2-x^3-x^4-x^5-x^6-x^7)*(1+x+x^2+x^3+x^4+x^5-x^7)) )); // G. C. Greubel, Oct 24 2022

Mathematica

f[x_]= -1 +x^2 +x^3 +x^4 +x^5 +x^6 +x^7;
CoefficientList[Series[-1/(x^7*f[x]*f[1/x]), {x,0,50}], x] (* G. C. Greubel, Oct 24 2022 *)

PARI

Vec(1/(1 +x -x^3 -2*x^4 -3*x^5 -5*x^6 -7*x^7 -5*x^8 -3*x^9 -2*x^10 -x^11 + x^13 +x^14) + O(x^40)) \\ Jinyuan Wang, Mar 10 2020

SageMath

def A147605_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^2-x^3-x^4-x^5-x^6-x^7)*(1+x+x^2+x^3+x^4+x^5-x^7)) ).list()
A147605_list(50) # G. C. Greubel, Oct 24 2022

Formula

G.f.: 1/(1 + x - x^3 - 2*x^4 - 3*x^5 - 5*x^6 - 7*x^7 - 5*x^8 - 3*x^9 - 2*x^10 - x^11 + x^13 + x^14).

G.f.: -1/(x^7*f(x)*f(1/x)), where f(x) = -1 + x^2 + x^3 + x^4 + x^5 + x^6 + x^7. - G. C. Greubel, Oct 24 2022

Extensions

Definition corrected by N. J. A. Sloane, Nov 09 2008